MINIMAL FREE RESOLUTIONS OF NUMERICAL SEMIGROUP ALGEBRAS VIA APÉRY SPECIALIZATION

Numerical semigroups with multiplicity m are parametrized by integer points in a polyhedral cone Cm, according to Kunz. For the toric ideal of any such semigroup, the main result here constructs a free resolution whose overall structure is identical for all semigroups parametrized by the relative interior of a fixed face of Cm. The matrix entries of this resolution are monomials whose exponents are parametrized by the coordinates of the corresponding point in Cm, and minimality of the resolution is achieved when the semigroup is of maximal embedding dimension, which is the case when it is parametrized by the interior of Cm itself.